## Wednesday, August 13, 2008

### Should you Brake, Slow Down or Go?

How fast would you need to be traveling towards a red traffic light to see it appear as green?

1. You're a little rusty on physics, and then you pull this question out?? Well, you asked for it...

The wavelength of green light is around 530 nm, yielding a frequency of 5.66*10^14 Hz (566 THz). Red light has an average wavelength of 685 nm, with a frequency of 438 THz. According to my graduate E&M book, the relativistic Doppler shift (different from the classical Doppler shift, since light travels the same speed in all inertial reference frames) is given by:

w' = gamma * w * (1-Beta*cos(theta))

w' = new frequency
w = old frequency
gamma = 1 / sqrt(1-Beta^2)
Beta = v/c
c = velocity of light
theta = angle between your velocity vector and that of the light (0 degrees in this case, assuming you're headed straight at the traffic light)

Plugging everything in:

566 = 438/sqrt(1-Beta^2)*(1-Beta)

and solving, yields:

Beta = -0.25

Therefore, you need to go 1/4 the speed of light, and the negative means you need to go the opposite direction of the light.

So you must go 1/4 the speed of light (about 75,000,000 m/s, or about 671,000,000 mph) toward the traffic light. I know my car can't go that fast ;-)

2. Abe -
I love reading your answers to these questions. Between you and Mike I am learning something everyday that I wouldn't have the opportunity to learn in my normal day to day.
Thanks guys!
Serena

3. As always abe, your answer is so much better than I could have said it.

Thanks!

4. I would just wait until it turns green ;)

5. Just watch out for those cameras!

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